A seller bought three different types of mobile covers, C1, C2, and C3. The ratio of their selling prices was 3:4:5. He made a profit of 25% on C1, 10% on C2, but incurred a loss of 20% on C3. What was his approximate percent gain or loss in the entire transaction?

Correct — B.
Take selling prices 300, 400, 500 (ratio 3 : 4 : 5).
C1, 25% profit: CP = 300 ÷ 1.25 = 240
C2, 10% profit: CP = 400 ÷ 1.10 = 363.64

C3, 20% loss: CP = 500 ÷ 0.80 = 625
Total CP = 240 + 363.64 + 625 = 1228.64
Total SP = 300 + 400 + 500 = 1200

Loss = 1228.64 − 1200 = 28.64
Loss % = 28.64 ÷ 1228.64 × 100 ≈ 2.33% → option (b)

Why the others are wrong

• (a)
  profit of 2.33% — Profit is the wrong direction. The covers cost 1228.64 parts and sell for 1200, so the seller is 28.64 parts down. The size, 2.33%, is right.
• (c)
  loss of 4.62% — 4.62% of the 1228.64 cost would be a loss of about 56.76 parts, nearly double the real shortfall of 1228.64 − 1200 = 28.64.
• (d)
  profit of 4.62% — Profit of 4.62% is wrong on both counts: total cost 1228.64 exceeds total sales 1200, and the gap is 2.33% of cost, not 4.62%.

When selling prices are given in a ratio, recover each cost by division: CP = SP ÷ (1 + profit rate) for a profit, CP = SP ÷ (1 − loss rate) for a loss.

The overall result compares total SP with total CP, and the percentage is taken on total cost. Here the 20% loss falls on the largest sale, C3, and costs 125 parts, more than the 60 + 36.36 earned on C1 and C2.

Key facts

• Profit of p%: CP = SP ÷ (1 + p⁄100).
• Loss of l%: CP = SP ÷ (1 − l⁄100).
• Overall profit or loss % = (total SP − total CP) ÷ total CP × 100.

Common traps

• Weighting the percentages by the selling-price ratio: (3 × 25 + 4 × 10 − 5 × 20) ÷ 12 = 1.25% profit, the wrong direction.
• Averaging the three percentages: (25 + 10 − 20) ÷ 3 = 5% profit.
• Finding C3's cost as 500 × 1.20 = 600 instead of 500 ÷ 0.80 = 625.

No directly related past PYQ was found.